Math Problem Statement

You can purchase a Treasury bill that is 107 days from maturity for $14,870. The Treasury bill has a face value of $15,000.

Round your answers to 3 decimal places. (e.g., 32.161)

a. Calculate the Treasury bill’s quoted yield.

Quoted Yield: %

Solution

To calculate the quoted yield on a Treasury bill, we can use the following formula:

Quoted Yield=(Face ValuePurchase PriceFace Value)×(360Days to Maturity)×100\text{Quoted Yield} = \left( \frac{\text{Face Value} - \text{Purchase Price}}{\text{Face Value}} \right) \times \left( \frac{360}{\text{Days to Maturity}} \right) \times 100

Given:

  • Face Value = $15,000
  • Purchase Price = $14,870
  • Days to Maturity = 107

Now, let's compute the quoted yield.

Quoted Yield=(15,00014,87015,000)×(360107)×100\text{Quoted Yield} = \left( \frac{15,000 - 14,870}{15,000} \right) \times \left( \frac{360}{107} \right) \times 100

I'll calculate that now.The Treasury bill's quoted yield is approximately 2.916%.

Would you like more details or have any questions?

Here are some related questions you might find useful:

  1. How does the quoted yield differ from the actual return on investment?
  2. What is the impact of the number of days to maturity on the yield?
  3. How do Treasury bills compare to Treasury bonds in terms of yield?
  4. What role does the 360-day year play in financial calculations like this one?
  5. How would the quoted yield change if the purchase price were different?

Tip: Treasury bills are typically considered low-risk investments because they are backed by the U.S. government, making them a popular choice for conservative investors.

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Math Problem Analysis

Mathematical Concepts

Finance
Yield Calculation
Percentage
Time Value of Money

Formulas

Quoted Yield = ((Face Value - Purchase Price) / Face Value) × (360 / Days to Maturity) × 100

Theorems

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Suitable Grade Level

College-level Finance